Dual arm manipulation of flexible objects

Cooperative manipulation stirs a great deal of interest due to the potential applications in industry. Most previous research work with multiple manipulators, however, focused on developing control strategies for the manipulation of rigid bodies. This research motivated by the growing interest as well in the manipulation of flexible objects seeks to develop simple yet practical and efficient control schemes that enable cooperating arms to handle a flexible beam. Specifically the problem studied herein is that of two arms rigidly grasping a flexible beam and such capable of generating forces/moments in such away as to move a flexible beam along a predefined trajectory. The major contribution of the thesis lies in the development of a sliding mode control law to control two identical arms handling a flexible beam that is modeled using B-spline approximation. Sliding mode control provides robustness against model imperfection and uncertainty. It also provides an implicit stability proof. Given the bounds of uncertainty in the model of the flexible beam and choosing a switching surface that enforces trajectory tracking, a control algorithm is designed to push the states to remain on the switching surface. While the system is in sliding mode, it will be forced to slide along or nearby the vicinity of the switching surface. The system is then robust and insensitive to the uncertainty associated with the fact that no information about the vibration dynamics is used in the controller (only measurable states are assumed to be known). Simulation results for two three joint arms moving a flexible beam are presented to validate the theoretical results. The thesis also provides analysis and simulation of a PD + internal force controller and an impedance control algorithm which are able to achieve set point position control. The PD controller and the impedance controller cannot (at least theoretically) enable one to achieve position tracking control.; The ability to compensate for the dynamics of the flexible beam using PD, impedance or sliding mode control coupled with the ability to control the internal forces enable one to execute certain tasks when manipulating flexible objects. To execute(say) a press-and-fit insertion, the desired motion and interaction forces are specified as dictated by the given task and accordingly controlled. Simulation results for two three joint arms moving a simple flexible object are presented to validate that fact.